Extrude faces seems to move faces and extrude outer edges
The hidden rules of Blender's operators can become so familiar that you don't notice them any more, and work round them / with them without noticing them. This is an example, for me, so it's interesting to have a look.

Trying to reduce it to the minimum case, Blender seems to use quite a simplistic rule to avoid the creation of internal faces when extruding regions, while still providing expected behavior when extruding simple, isolated shapes.



In this example, we start with two squares. One has a connected face extending one side.


The pink and blue faces were extruded downwards in separate operations. The pink extrusion left a face behind, the blue one didn't. This suggests Blender's rule is to duplicate a region of faces only if none of the edges surrounding it are shared  by another face.
Sure enough, the green faces were extruded in one operation. Still, the extrusion didn't leave a face behind, even in the isolated region. So the rule seems to be not to duplicate faces if any bounding edge of the selection is shared. (This applies even if you try setting the extrude to 'Individual Faces')


So it's not something funny you've done. Your best route to where you want to go is probably to select the edges on the outside perimeter of your base, EZ them downward, and F fill the bottom end. Or, work in one direction, from the bottom up,I insetting on the way.